List.length_replicate: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend as List
Lines 46-51 of bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&start_line=46&end_line=51

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def length_replicate(-A: Data, +n: Nat, +x: A) -> {SC.length(A, SC.replicate(A, n, x)) == n : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+p:
      N.succ_cong(SC.length(A, SC.replicate(A, p, x)), p, length_replicate(A, p, x))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=replicate